Method of eliminating scaling errors in analog computation



Aag. 1s, 1959 VOL 706 soa/ece Y VOL THG-E E. RAWDIN METHOD OF ELIMINATING SCALING ERRORS IN ANALOG COMPUTATION Filed Aug. 13, 1957 @MMM/5e g METHOD OF ELIMHWATING SCALING ERRORS IN ANALOG COMPUTATION Eugene Rawdin, Levittown, Pa., assigner to the United States of America as represented by the Secretary of the Air Force Application August 13, 1957, Serial No. 678,023 3 Claims. (cl. 179;-171) (Granted under Title 35, U.S. Code (1952), sec. 266) The invention described herein may be manufactured and used by or for the United States Government for governmental purposes without payment to me of any royalty thereon.

This invention relates to negative feedback amplifiers as used in analog computers and particularly those ampliers that derive their inputs from adjustable scaling potentiometers.

Amplifiers used in analog circuits usually are supplied with sufficient negative feedback to render the gain independent of changes in supply voltage, tube characteristics, etc., so as to eliminate errors from these causes. However, if the amplier derives its input from an adjustable potentiometer, as is often the case in scaling circuits, the input potentiometer becomes a part of the feedback path with the result that adjustment of the potentiometer varies the feedback and therefore the gain of the amplifier. It is the object of the invention to prevent errors from this source. Briefly, this is accomplished by providing an adjustable attenuating network in the feedback path that is electrically similar to the input potentiometer as it appears in the feedback path, and gauging the adjusting mechanisms so that the inserted network varies the feedback in a manner equal and opposite to the variation in feedback produced by the input potentiometer.

A more detailed description of the invention will be given in connection with the specific embodiments thereof shown in the accompanying drawings in which Fig. 1 shows a conventional negative feedback amplifier having an adjustable potentiometer in its input circuit,

Fig. 2 illustrates the invention applied to the amplifier of Fig. 1, and

Fig. 3 is a modification of Fig. 2.

As is known, the gain of an amplifier with negative feedback is expressed by the following equation:

Since B is independent of such factors as tube characteristics, supply voltages, etc., changes in these factors will notv affect the gain of the amplifier.

l Gris In the amplifier circuit of Fig. 1, the factor B, or the fraction of the voltage E0 appearing at the output terminal b of amplifier 1 that is fed back to the input terminal a of the amplifier, assuming the internal impedance of voltage source 2 to be negligible, is

When contact 3 in Fig. 1 is moved along the potentiometer resistance element, the quantity Zvi-Z2 varies which, as seen from Equation 3, causes a 'variation in B which in turn, as seen in Equations 1 andI 2, causes a variation in the gain G of the amplifier and a consequent error in E0.

In accordance with the invention this error is prevented by making B a constantindependent of the position of contact 3. This is accomplished by inserting an adjustable potentiometer` having a resi-stance element Z1'}-Z2 in series with Z4 in the feedback circuit as shown in Fig. 2. The value of B is now given Iby the expression and if the contacts 3 and 4 are ganged by a mechanical coupling 5 so that maza-Zafra Substituting this value in Equation 4 or, simplifying (8),

the gain of any negative feedback amplier employing the invention is" variations in powerv supply voltage, tube characteristics and other factors 'that may affect A.

In Fig. 2, it was assumed that the impedance of voltage source. Z was negligible in comparison with the other impedances, particularly Z3. If this is not the case the 25 internal impedance Zs of source 2 must be taken into account. This can be done by` connecting an impedance Za' in shunt to Z1'Z2, as shown in Fig. 3. The expression for B in thissituationbecomes and if, as before, contacts 3 and 4 are ganged so that Substituting this value in E quation 12 Rearranging (16) 3' Z1+Zz+zs p *Y e5 from which 1 Z3'. Big# fzlJfZs 70 This is seen to agree with Equation 9' so that the expressions for amplifierk gain given inA Equations l0 and ll aplyi-- As demonstrated above, the effect of the lnventlon 1s toz make B, a; constant andi independentofthe position of 76 i contact 3. In other Words, the invention maintains the ratio Z1(Z2|Z) ZSJVZHFZZJVZs Z1(Z2+Zs) Z1(Z2-i-Z2) Z4+Zy+z2f+zg+Z3+Z1+Z2+Zs which is the definition of B, constant. From the laws of proportionality, if the above ratio is constant the ratio Z1(Z2l-Zt) Zwaan/+L' Z1 Z2iZs Z 3+Z1+z2+zs is constant. 'Ihis may be proven by substituting in the above ratio the value from Equation l5, giving the ratio Z4 EZIJVZZJVZS Z1 Z2 'i' Z s) Z3+Z1+z2+z, which reduces to the constant Therefore, from another viewpoint, the invention operates to maintain the ratio of the impedance between terminals a-b to the impedance between terminal a and ground constant and independent of the position of con-Y tact 3. When this condition exists, B is independent of the. position of contact 3 as desired.

. I claim:

l. An amplifier having an input terminal, an outputput and input terminals; and means for making the fraction of the voltage at said output terminal fed back to said input terminal independent of the position of said tap, said means comprising: a two-terminal network connected in said feedback circuit; said network comprising a second impedance element having an adjustable tap, said tapbeing connected to one network terminal, one end of said second impedance element being connected to the other network terminal, and the other end of said second impedance element being connected to said otherV network terminal through a third impedance proportional to the impedance of said signal source; and means for gauging the taps of said first and second impedance elements for simultaneous adjustment.

2. Apparatus as claimed in claim l in which the ratio of said second impedance to said first impedance equals the ratio of said third impedance to the impedance of saidr signal source, and in which the gauging of said taps is such as tomaintain the ratio of impedances on either side of the tap on said second impedance equal to the ratio of mpedances on either side of the tap on said first impedance.

3. An amplifier having an input terminal, an output terminal and a common terminal; a signal level adjusting potentiometer comprising a first impedance element and said means comprising: a two-termina1 network connected in said feedback circuit in series with said third impedance, said network comprising a fourth impedance element having the same ratio to said rst impedance element that said third impedance has to said second impedance, said fourth impedance element having an adjustable tap connected to one of said network terminals, one end of said fourth impedance element being connected to the other network terminal, and the other end of said fourth impedance element being connected to said other network terminal through a fifth impedance having -a ratio to the impedance of said signal source equal to the ratio of said third impedance to said second impedance; and means for gauging the taps of said rst and fourth impedance elements for simultaneous adjustment, said gauging being such -as to maintain the ratio of impedances on either side of the tap on said fourth impedance element equal to the ratio of impedances on 5 either side of the tap on said rst impedance element.

vReferences Cited in the tile of this patent UNITED STATES PATENTS 

